数学最新文献

{"title":"Estimating singular functions of kernel cross-covariance operators: An investigation of the Nyström method","authors":"Min Xu ,&nbsp;Qi-Hang Zhou ,&nbsp;Qin Fang ,&nbsp;Zhuo-Xi Shi","doi":"10.1016/j.jmva.2025.105514","DOIUrl":"10.1016/j.jmva.2025.105514","url":null,"abstract":"<div><div>We investigate the Nyström method as an efficient means of overcoming the computational bottleneck inherent in estimating the singular functions of kernel cross-covariance operators, which play a central role in tasks such as covariate shift correction and multi-view learning. We present a Nyström-type approximation of the kernel cross-covariance operator, and establish its convergence rate. Furthermore, we derive a novel bound on the weighted sum of squared estimation errors of all associated singular functions, providing tighter control than traditional bounds that treat each error individually. Our theoretical analysis reveals that the Nyström-based singular function estimators attain the same statistical accuracy as their full empirical counterparts, while offering significant computational savings. Numerical experiments further confirm the practical effectiveness of the proposed approach.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105514"},"PeriodicalIF":1.4,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterization of q-solitons under trace conditions and conformal vector fields","authors":"Antonio W. Cunha ,&nbsp;Antonio N. Silva Jr. ,&nbsp;Rahul Poddar","doi":"10.1016/j.bulsci.2025.103746","DOIUrl":"10.1016/j.bulsci.2025.103746","url":null,"abstract":"<div><div>We investigate gradient <em>q</em>-solitons <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> characterized by a non-positive or non-negative trace of the structure tensor <em>q</em>. Through the imposition of specific regularity conditions on the potential function <em>f</em>, we deduce that <em>M</em> is both stationary and <em>q</em>-flat, consequently rendering it trivial. In the non-gradient case, we assume a contracted Bianchi type condition and prove certain characterizations of <em>q</em>-solitons <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>X</mi><mo>)</mo></math></span> when the vector field <em>X</em> is conformal. Our results showcase versatility as we apply them to solitons associated with diverse geometric flows.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103746"},"PeriodicalIF":0.9,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a class of complete permutation quadrinomials","authors":"Chin Hei Chan ,&nbsp;Zhiguo Ding ,&nbsp;Nian Li ,&nbsp;Xi Xie ,&nbsp;Maosheng Xiong ,&nbsp;Michael E. Zieve","doi":"10.1016/j.ffa.2025.102734","DOIUrl":"10.1016/j.ffa.2025.102734","url":null,"abstract":"<div><div>Let <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn><mi>q</mi></mrow></msup><mo>+</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn><mi>q</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>q</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>d</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub><mo>[</mo><mi>x</mi><mo>]</mo></math></span>, where <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> is the finite field of order <span><math><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><mi>q</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup></math></span> for some positive integer <em>m</em>. Tu et al. (Finite Fields Appl. 68: 1-20, 2020) proposed a sufficient condition under which <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is a complete permutation on <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>. In this paper, we show that this sufficient condition is also necessary, and when <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is a complete permutation, then <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> and <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>x</mi></math></span> are simultaneously linear equivalent to <span><math><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mover><mrow><mi>x</mi></mrow><mo>‾</mo></mover></math></span> and <span><math><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mover><mrow><mi>x</mi></mrow><mo>‾</mo></mover><mo>+</mo><mi>γ</mi><mi>x</mi></math></span> for some <span><math><mi>γ</mi><mo>∈</mo><msubsup><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span> satisfying <span><math><mrow><mi>ord</mi></mrow><mo>(</mo><msup><mrow><mi>γ</mi></mrow><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo><mo>=</mo><mn>3</mn></math></span>. This result leads to a complete characterization of the complete permutation quadrinomials of the above form <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"110 ","pages":"Article 102734"},"PeriodicalIF":1.2,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Metricity of the Chatterjee Correlation Coefficient","authors":"Flavio Chierichetti, Mirko Giacchini, Ravi Kumar","doi":"10.1080/00031305.2025.2571183","DOIUrl":"https://doi.org/10.1080/00031305.2025.2571183","url":null,"abstract":"We show that the distance measure implied by the recently proposed Chatterjee coefficient of correlation can violate the triangle inequality, both in theory and in practice.","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"10 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145255058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A proof of a version of Griggs and Yeh’s conjecture for L(2,1)-labeling of iterated Mycielskians","authors":"Kamal Dliou ,&nbsp;Hicham El Boujaoui ,&nbsp;Dwi Agustin Retnowardani","doi":"10.1016/j.dam.2025.10.011","DOIUrl":"10.1016/j.dam.2025.10.011","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In a graph &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, a function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; from the vertex set &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; to the set of all nonnegative integers is called an &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;-labeling of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, if it satisfies the following conditions for any two vertices &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; denotes the distance between the vertices &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; in &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The span of &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is the difference between the largest and the smallest label used by &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;-labeling number of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is the minimum span over all &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;-labelings of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, it is denoted by &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. In 1992, Griggs and Yeh conjectured that for any graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of maximum degree &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, the inequality &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 516-522"},"PeriodicalIF":1.0,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the matching problem in random hypergraphs","authors":"Peter Frankl ,&nbsp;Jiaxi Nie ,&nbsp;Jian Wang","doi":"10.1016/j.disc.2025.114839","DOIUrl":"10.1016/j.disc.2025.114839","url":null,"abstract":"<div><div>We study a variant of the Erdős Matching Problem in random hypergraphs. Let <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span> denote the Erdős-Rényi random <em>k</em>-uniform hypergraph on <em>n</em> vertices where each possible edge is included with probability <em>p</em>. We show that when <span><math><mi>n</mi><mo>≫</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>s</mi></math></span> and <em>p</em> is not too small, with high probability, the maximum number of edges in a sub-hypergraph of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span> with matching number <em>s</em> is obtained by the trivial sub-hypergraphs, i.e. the sub-hypergraph consisting of all edges containing at least one vertex in a fixed set of <em>s</em> vertices.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 3","pages":"Article 114839"},"PeriodicalIF":0.7,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Resolvent estimates for the one-dimensional damped wave equation with unbounded damping","authors":"Antonio Arnal","doi":"10.1016/j.na.2025.113978","DOIUrl":"10.1016/j.na.2025.113978","url":null,"abstract":"<div><div>We study the generator <span><math><mi>G</mi></math></span> of the one-dimensional damped wave equation with unbounded damping at infinity. We show that the norm of the corresponding resolvent operator, <span><math><mrow><mo>‖</mo><msup><mrow><mrow><mo>(</mo><mi>G</mi><mo>−</mo><mi>λ</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>‖</mo></mrow></math></span>, is approximately constant as <span><math><mrow><mrow><mo>|</mo><mi>λ</mi><mo>|</mo></mrow><mo>→</mo><mo>+</mo><mi>∞</mi></mrow></math></span> on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane, <span><math><mrow><msub><mrow><mover><mrow><mi>ℂ</mi></mrow><mo>¯</mo></mover></mrow><mrow><mo>−</mo></mrow></msub><mo>≔</mo><mrow><mo>{</mo><mi>λ</mi><mo>∈</mo><mi>ℂ</mi><mo>:</mo><mo>Re</mo><mi>λ</mi><mo>≤</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span>. Our proof rests on a precise asymptotic analysis of the norm of the inverse of <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></mrow></math></span>, the quadratic operator associated with <span><math><mi>G</mi></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113978"},"PeriodicalIF":1.3,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The impact of higher-order dynamics with intraspecific competition in replicator dynamics on species stability","authors":"Wenhao She ,&nbsp;Yali Zhang ,&nbsp;Yikang Lu ,&nbsp;Haiying Wu ,&nbsp;Lei Shi ,&nbsp;Junpyo Park","doi":"10.1016/j.chaos.2025.117364","DOIUrl":"10.1016/j.chaos.2025.117364","url":null,"abstract":"<div><div>Higher-order interactions, as crucial factors in natural ecosystems, can be prominently observable across diverse ecological systems. Previous studies have predominantly focused on pairwise interspecific interactions. In this work, we investigate how higher-order interactions (HOI) and intraspecific competition jointly influence ecosystem stability in a rock–paper–scissors (RPS) model by incorporating intraspecific competition factors into a replicator dynamics framework that integrates both pairwise and higher-order interactions. Our findings reveal that the system undergoes a Hopf bifurcation within specific parameter ranges, generating a subcritical limit cycle manifested as periodic oscillations in species abundance. Conversely, the system traverses the Hopf bifurcation when critical parameters exceed threshold values, driving all species toward extinction via boundary attractors. Notably, the strength of intraspecific competition significantly modulates system stability, and under specific combinations of intensities influences system dynamics and the properties of limit cycles. Our study highlights the importance of incorporating multidimensional intraspecific competition into game-theoretic models with higher-order interactions to understand biodiversity maintenance and ecosystem stability. We hope this work may provide novel theoretical insights into the multidimensional effects of intra- and inter-species interactions in complex ecological networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117364"},"PeriodicalIF":5.6,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An IMEX scheme for a nonlinear PDE model of tumor angiogenesis","authors":"Pasquale De Luca,&nbsp;Livia Marcellino","doi":"10.1016/j.cam.2025.117139","DOIUrl":"10.1016/j.cam.2025.117139","url":null,"abstract":"<div><div>This paper presents a numerical analysis of an Implicit–Explicit scheme for a non-linear parabolic PDE model of tumor angiogenesis. The model describes the evolution of endothelial cells, proteases, inhibitors, and extracellular matrix through coupled equations incorporating diffusion, chemotaxis, haptotaxis, and reaction kinetics. We design a numerical approach that manages stiff linear terms implicitly while handling non-stiff nonlinear terms explicitly. Theoretical analysis establishes main features of the scheme such as stability properties, second-order convergence, and preservation of conservation laws. Moreover, the computational complexity is analyzed, demonstrating an efficiency gains compared to fully explicit methods. Numerical experiments validate these findings and show the ability of the method to accurately capture complex biological phenomena.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"476 ","pages":"Article 117139"},"PeriodicalIF":2.6,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal planar immersions of prescribed winding number and Arnold invariants","authors":"Anna Lagemann,&nbsp;Heiko von der Mosel","doi":"10.1016/j.na.2025.113942","DOIUrl":"10.1016/j.na.2025.113942","url":null,"abstract":"<div><div>Vladimir Arnold defined three invariants for generic planar immersions, i.e. planar curves whose self-intersections are all transverse double points. We use a variational approach to study these invariants by investigating a suitably truncated knot energy, the tangent-point energy. We prove existence of energy minimizers for each truncation parameter <span><math><mrow><mi>δ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> in a class of immersions with prescribed winding number and Arnold invariants, and establish Gamma convergence of the truncated tangent-point energies to a limiting renormalized tangent-point energy as <span><math><mrow><mi>δ</mi><mo>→</mo><mn>0</mn></mrow></math></span>. Moreover, we show that any sequence of minimizers subconverges in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, and the corresponding limit curve has the same topological invariants, self-intersects exclusively at right angles, and minimizes the renormalized tangent-point energy among all curves with right self-intersection angles. In addition, the limit curve is an almost-minimizer for all of the original truncated tangent-point energies as long as the truncation parameter <span><math><mi>δ</mi></math></span> is sufficiently small. Therefore, this limit curve serves as an “optimal” curve in the class of generic planar immersions with prescribed winding number and Arnold invariants.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113942"},"PeriodicalIF":1.3,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}